Infrared divergence in d.c. Josephson current through charge density wave

K. Sano; S. Kurihara

doi:10.1016/S0921-4534(00)01626-9

Infrared divergence in d.c. Josephson current through charge density wave

K. Sano^*, S. Kurihara

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S₁, S₂) by tunnel junctions. At T = 0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d/v_F ≫ ℏ/Δ_S, ℏ/Δ_CDW where T is temperature. These limits are expressed by using the energy gap in S region Δ_S, the length d, the Fermi velocity v_F, and the energy gap Δ_CDW in CDW region. The critical current is proportional to (Δ_CDWℏv_F/d)^1/2 ∝ Δ_CDW(ξ_CDW/d)^1/2. At βΔ_S(T), βΔ_CDW(T) ≫ 1 and βℏv_F/d ≪ 1, the T-dependence of the correction caused by the phase mode is T-linear where β = 1/k_BT and k_B is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T. At finite temperatures and without impurities, the critical current is similar to the Ambegaokar-Baratoff formula which is proportional to Δ_S(T) in the short-junction limit: d/v_F ≪ ℏ/Δ_S, ℏ/Δ_CDW.

Original language	English
Pages (from-to)	308-322
Number of pages	15
Journal	Physica C: Superconductivity and its Applications
Volume	351
Issue number	3
DOIs	https://doi.org/10.1016/S0921-4534(00)01626-9
Publication status	Published - 2001 Apr 1

Keywords

Charge density wave
Critical current density
Josephson current

ASJC Scopus subject areas

Condensed Matter Physics

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10.1016/S0921-4534(00)01626-9

Cite this

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title = "Infrared divergence in d.c. Josephson current through charge density wave",

abstract = "We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S1, S2) by tunnel junctions. At T = 0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d/vF ≫ ℏ/ΔS, ℏ/ΔCDW where T is temperature. These limits are expressed by using the energy gap in S region ΔS, the length d, the Fermi velocity vF, and the energy gap ΔCDW in CDW region. The critical current is proportional to (ΔCDWℏvF/d)1/2 ∝ ΔCDW(ξCDW/d)1/2. At βΔS(T), βΔCDW(T) ≫ 1 and βℏvF/d ≪ 1, the T-dependence of the correction caused by the phase mode is T-linear where β = 1/kBT and kB is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T. At finite temperatures and without impurities, the critical current is similar to the Ambegaokar-Baratoff formula which is proportional to ΔS(T) in the short-junction limit: d/vF ≪ ℏ/ΔS, ℏ/ΔCDW.",

keywords = "Charge density wave, Critical current density, Josephson current",

author = "K. Sano and S. Kurihara",

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TY - JOUR

T1 - Infrared divergence in d.c. Josephson current through charge density wave

AU - Sano, K.

AU - Kurihara, S.

PY - 2001/4/1

Y1 - 2001/4/1

N2 - We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S1, S2) by tunnel junctions. At T = 0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d/vF ≫ ℏ/ΔS, ℏ/ΔCDW where T is temperature. These limits are expressed by using the energy gap in S region ΔS, the length d, the Fermi velocity vF, and the energy gap ΔCDW in CDW region. The critical current is proportional to (ΔCDWℏvF/d)1/2 ∝ ΔCDW(ξCDW/d)1/2. At βΔS(T), βΔCDW(T) ≫ 1 and βℏvF/d ≪ 1, the T-dependence of the correction caused by the phase mode is T-linear where β = 1/kBT and kB is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T. At finite temperatures and without impurities, the critical current is similar to the Ambegaokar-Baratoff formula which is proportional to ΔS(T) in the short-junction limit: d/vF ≪ ℏ/ΔS, ℏ/ΔCDW.

AB - We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S1, S2) by tunnel junctions. At T = 0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d/vF ≫ ℏ/ΔS, ℏ/ΔCDW where T is temperature. These limits are expressed by using the energy gap in S region ΔS, the length d, the Fermi velocity vF, and the energy gap ΔCDW in CDW region. The critical current is proportional to (ΔCDWℏvF/d)1/2 ∝ ΔCDW(ξCDW/d)1/2. At βΔS(T), βΔCDW(T) ≫ 1 and βℏvF/d ≪ 1, the T-dependence of the correction caused by the phase mode is T-linear where β = 1/kBT and kB is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T. At finite temperatures and without impurities, the critical current is similar to the Ambegaokar-Baratoff formula which is proportional to ΔS(T) in the short-junction limit: d/vF ≪ ℏ/ΔS, ℏ/ΔCDW.

KW - Charge density wave

KW - Critical current density

KW - Josephson current

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Infrared divergence in d.c. Josephson current through charge density wave

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